COALESCENCE OF UPPER AND LOWER MISCIBILITY GAPS IN SYSTEMS WITH CONCENTRATION-DEPENDENT INTERACTIONS

The merging of upper and lower critical solution temperature miscibility gaps is investigated theoretically for binary systems whose interaction parameter g depends strongly on concentration. The process is called forth by increasing the chain lengths m1 and m2 of both components while keeping their ratio m2/m1 constant. The principal mechanisms of merging, referred to as sideways coalescence, seem to be different for systems symmetric (m2 = m1) and asymmetric (m2 = 2m1) in molecular size. However, both displayed pattern sequences should be representative of small-molecule mixtures as well as polymer blends. Literature data on miscibility gaps and heats of mixing in the system chlorinated polyethylene/poly(methyl methacrylate) point to the relevance of the theoretical considerations. Furthermore, criteria for various landmark situations are derived in terms of concentration (phi-2) and temperature (T) derivatives of the interaction function g(phi-2,T). For instance, depending on g(phi-2, T), the boundary between the LCST and UCST behavior in T vs phi-2 plane may be not only horizontal (as customary) but also vertical, or, in general, inclined. The binodal slope, dT/d-phi-2, can be rigorously related to the spinodal function, and the result utilized for pinpointing the moment of sideways coalescence between the two gaps. Also, the condition is derived for the singular point marking the transition between two types of binodal patterns.